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On dual hyperovals of rank 4 over \({{\mathbb{F}}_2}\)

Journal of Geometry volume 108, pages 75–98 (2017)Cite this article

Abstract

We discuss dual hyperovals of rank 4 over \({{\mathbb{F}}_2}\). In particular, we classify all such dual hyperovals if the ambient space has dimension 7 or 8. We also determine the bilinear dual hyperovals in the case of an ambient space of dimension 9 or 10. A classification of all dual hyperovals in dimension 9 seems possible in the near future.

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Authors and Affiliations

  1. Department of Mathematics, Colorado State University, Fort Collins, CO, 80523, USA

    Anton Betten

  2. Department of Mathematics, University of Kaiserslautern, Kaiserslautern, Germany

    Ulrich Dempwolff

  3. Department of Mathematics, University of Bayreuth, Bayreuth, Germany

    Alfred Wassermann

Authors
  1. Anton Betten
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  2. Ulrich Dempwolff
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  3. Alfred Wassermann
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Correspondence to Anton Betten.

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Betten, A., Dempwolff, U. & Wassermann, A. On dual hyperovals of rank 4 over \({{\mathbb{F}}_2}\) . J. Geom. 108, 75–98 (2017). https://doi.org/10.1007/s00022-016-0326-2

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  • DOI: https://doi.org/10.1007/s00022-016-0326-2

Mathematics Subject Classification

  • 51E21

Keywords

  • Dual hyperoval
  • enumeration
  • finite projective geometry